# Takayuki Kihara: Recursion theoretic methods in topological dimension theory

Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 26 November 2014, 17:30 hrs

Room: S17#04-05, Department of Mathematics, NUS

Speaker: Takayuki Kihara

Title: Recursion theoretic methods in topological dimension theory

URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html

Abstract:
By introducing the notion of generalized Turing degrees in any
admissibly represented space (represented second-countable T0-quotient
space), we provide a refinement of Roman Pol’s solution to Pavel
Alexandrov’s old problem in infinite dimensional topology. Formally,
we show that there is an embedding of an uncountable partial ordering
into the sigma-embeddability ordering of weakly infinite dimensional
metrizable compacta (indeed, metrizable C-compacta, also known as
selectively screenable compacta Sc(O,O) in set theoretic topology).
This is a joint work with Arno Pauly (Univ. Cambridge, UK).